Subgroups — C₁₃×#26406 #15712745

Order 3328.

714 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2060	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1866	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₁₃×#544	C₂²	1	1	yes	characteristic
19	C₁₃×#520	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#519	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	1	no	—
23	C₁₃×#479	—	2	1	no	—
24	C₁₃×#479	—	2	1	no	—
25	C₁₃×#478	—	2	1	no	—
26	C₁₃×#477	—	2	1	no	—
27	C₁₃×#477	—	2	1	no	—
28	C₁₃×#475	—	2	1	no	—
29	C₁₃×#474	—	2	1	no	—
30	C₁₃×#441	—	2	1	no	—
31	C₁₃×#440	—	2	1	no	—
32	C₄×C₁₃×Q₁₆	—	2	1	no	—
33	C₄×C₁₃×SD₁₆	—	2	1	no	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₁₃×#428	—	2	1	no	—
36	C₁₃×#428	—	2	1	no	—
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	—	2	1	no	—
43	C₁₃×#427	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#107	—	2	1	no	—
45	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
47	C₁₃×#424	C₂²	1	1	yes	characteristic
48	C₁₃×#424	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₁₃×#419	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#416	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₁₃×#405	C₂²	1	1	yes	characteristic
57	C₁₃×#391	C₂²	1	1	yes	characteristic
58	C₁₃×#384	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#341	C₂²	1	1	yes	characteristic
63	C₁₃×#339	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#336	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#137	—	2	2	no	—
70	C₁₃×#137	Q₈	1	4	yes	complemented
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₁₃×#131	—	2	2	no	—
74	C₁₃×#131	—	2	2	no	—
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×#125	—	2	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	4	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	4	1	no	—
97	C₄×D₄×C₁₃	—	4	1	no	—
98	C₁₃×#117	—	2	1	no	—
99	C₁₃×#117	—	2	1	no	—
100	C₁₃×#117	—	4	1	no	—
101	C₁₃×#117	C₂³	1	1	yes	characteristic
102	C₁₃×#117	C₂³	1	1	yes	characteristic
103	C₁₃×#117	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#108	—	2	2	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	2	1	no	—
116	C₁₃×#107	—	2	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	1	no	—
121	C₁₃×#107	D₄	1	1	yes	characteristic
122	C₁₃×#107	D₄	1	1	yes	characteristic
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×#106	—	2	1	no	—
127	C₁₃×#106	—	2	1	no	—
128	C₁₃×#106	D₄	1	1	yes	characteristic
129	C₁₃×#106	D₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₈	—	2	1	no	—
131	C₁₃×C₄⋊C₈	—	2	1	no	—
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×C₄⋊C₈	—	2	1	no	—
134	C₁₃×#104	—	2	2	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	—	2	1	no	—
138	C₁₃×#103	—	2	1	no	—
139	C₁₃×#103	—	2	1	no	—
140	C₁₃×#103	—	2	1	no	—
141	C₁₃×#103	—	2	1	no	—
142	C₁₃×#103	D₄	1	1	yes	characteristic
143	C₁₃×#103	D₄	1	1	yes	characteristic
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	D₄	1	1	yes	characteristic
146	C₁₃×#102	D₄	1	1	yes	characteristic
147	C₁₃×#101	—	2	2	no	—
148	C₁₃×#97	—	2	1	no	—
149	C₄×C₈×C₁₃	—	2	1	no	—
150	C₁₃×#95	—	4	1	no	—
151	#26406	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₁₃×#41	—	2	1	no	—
153	C₁₃×#41	—	2	1	no	—
154	C₁₃×#41	C₂×Q₈	1	2	yes	—
155	C₁₃×#41	#41	1	2	yes	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	4	1	no	—
162	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	4	1	no	—
173	C₂²×C₄×C₁₃	—	4	1	no	—
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₁₃×Q₁₆	—	2	4	no	—
176	C₁₃×SD₁₆	—	2	4	no	—
177	C₁₃×M₁₆	—	2	4	no	—
178	C₁₃×M₁₆	—	2	1	no	—
179	C₁₃×M₁₆	—	2	1	no	—
180	C₁₃×M₁₆	—	2	1	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	—	2	1	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
185	C₁₃×M₁₆	#41	1	2	yes	—
186	C₂×C₈×C₁₃	—	2	4	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	4	1	no	—
206	C₁₃×C₄⋊C₄	—	4	1	no	—
207	C₁₃×C₄⋊C₄	—	4	1	no	—
208	C₁₃×C₄⋊C₄	—	4	1	no	—
209	C₁₃×C₄⋊C₄	—	4	1	no	—
210	C₁₃×C₄⋊C₄	—	4	1	no	—
211	C₁₃×C₄⋊C₄	—	4	1	no	—
212	C₁₃×C₄⋊C₄	—	8	2	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	2	1	no	—
221	C₁₃×C₂²⋊C₄	—	2	1	no	—
222	C₁₃×C₂²⋊C₄	—	4	1	no	—
223	C₁₃×C₂²⋊C₄	—	4	1	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	4	1	no	—
230	C₄²×C₁₃	—	4	1	no	—
231	C₄²×C₁₃	—	4	1	no	—
232	C₄²×C₁₃	—	4	1	no	—
233	#3083	C₂×C₁₃	1	1	yes	characteristic
234	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2947	C₂×C₁₃	1	1	yes	characteristic
236	#2913	C₂×C₁₃	1	1	yes	characteristic
237	#2095	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2060	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1922	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1908	C₂×C₁₃	1	1	yes	characteristic
244	#1882	C₂×C₁₃	1	1	yes	characteristic
245	#1866	C₂×C₁₃	1	1	yes	characteristic
246	#1859	C₂×C₁₃	1	1	yes	characteristic
247	#1857	C₂×C₁₃	1	1	yes	characteristic, complemented
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
250	Q₈×C₁₃	—	2	1	no	—
251	Q₈×C₁₃	—	2	2	no	—
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	4	1	no	—
254	Q₈×C₁₃	—	4	1	no	—
255	Q₈×C₁₃	—	16	1	no	—
256	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	1	no	—
260	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	8	1	no	—
280	C₂×C₄×C₁₃	—	8	1	no	—
281	C₂×C₄×C₁₃	—	8	1	no	—
282	C₂×C₄×C₁₃	—	16	1	no	—
283	C₂×C₄×C₁₃	—	16	1	no	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
290	C₈×C₁₃	—	2	2	no	—
291	C₈×C₁₃	—	2	1	no	—
292	C₈×C₁₃	—	2	2	no	—
293	C₈×C₁₃	—	2	1	no	—
294	C₈×C₁₃	—	2	1	no	—
295	C₈×C₁₃	—	2	1	no	—
296	C₈×C₁₃	—	4	1	no	—
297	C₈×C₁₃	—	4	1	no	—
298	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
300	#544	C₂²×C₁₃	1	1	yes	characteristic
301	#520	C₂²×C₁₃	1	1	yes	characteristic
302	#520	C₂²×C₁₃	1	1	yes	characteristic
303	#519	C₂²×C₁₃	1	1	yes	characteristic
304	#479	—	2	1	no	—
305	#479	—	2	1	no	—
306	#479	—	2	1	no	—
307	#478	—	2	1	no	—
308	#477	—	2	1	no	—
309	#477	—	2	1	no	—
310	#475	—	2	1	no	—
311	#474	—	2	1	no	—
312	#441	—	2	1	no	—
313	#440	—	2	1	no	—
314	C₄×Q₁₆	—	2	1	no	—
315	C₄×SD₁₆	—	2	1	no	—
316	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
317	#428	—	2	1	no	—
318	#428	—	2	1	no	—
319	#428	C₂²×C₁₃	1	1	yes	characteristic
320	#428	C₂²×C₁₃	1	1	yes	characteristic
321	#428	C₂²×C₁₃	1	1	yes	characteristic
322	#428	C₂²×C₁₃	1	1	yes	characteristic
323	#428	C₂²×C₁₃	1	1	yes	characteristic
324	#427	—	2	1	no	—
325	#427	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#107	—	2	1	no	—
327	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
329	#424	C₂²×C₁₃	1	1	yes	characteristic
330	#424	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
332	#419	C₂²×C₁₃	1	1	yes	characteristic
333	#417	C₂²×C₁₃	1	1	yes	characteristic
334	#416	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
338	#405	C₂²×C₁₃	1	1	yes	characteristic
339	#391	C₂²×C₁₃	1	1	yes	characteristic
340	#384	C₂²×C₁₃	1	1	yes	characteristic
341	#343	C₂²×C₁₃	1	1	yes	characteristic
342	#343	C₂²×C₁₃	1	1	yes	characteristic
343	#343	C₂²×C₁₃	1	1	yes	characteristic
344	#341	C₂²×C₁₃	1	1	yes	characteristic
345	#339	C₂²×C₁₃	1	1	yes	characteristic
346	#339	C₂²×C₁₃	1	1	yes	characteristic
347	#339	C₂²×C₁₃	1	1	yes	characteristic
348	#336	C₂²×C₁₃	1	1	yes	characteristic
349	C₂²×C₁₃	—	2	1	no	—
350	C₂²×C₁₃	—	2	1	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	4	1	no	—
354	C₂²×C₁₃	#539	1	1	yes	characteristic
355	C₂²×C₁₃	D₄²	1	1	yes	characteristic
356	C₂²×C₁₃	#554	1	1	yes	characteristic
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	2	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	4	1	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	—	8	1	no	—
369	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
370	C₄×C₁₃	#525	1	1	yes	characteristic
371	C₄×C₁₃	#547	1	1	yes	characteristic
372	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
373	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
375	#137	—	2	2	no	—
376	#137	Q₈×C₁₃	1	4	yes	complemented
377	C₂×Q₁₆	—	2	1	no	—
378	C₂×SD₁₆	—	2	1	no	—
379	#131	—	2	2	no	—
380	#131	—	2	2	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₄⋊Q₈	—	2	1	no	—
390	C₄⋊Q₈	—	2	1	no	—
391	#125	—	2	1	no	—
392	#125	—	2	1	no	—
393	C₂²⋊Q₈	—	4	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	4	1	no	—
403	C₄×D₄	—	4	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	—	4	1	no	—
407	#117	C₂³×C₁₃	1	1	yes	characteristic
408	#117	C₂³×C₁₃	1	1	yes	characteristic
409	#117	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	4	1	no	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	#108	—	2	2	no	—
418	#107	—	2	1	no	—
419	#107	—	2	1	no	—
420	#107	—	2	1	no	—
421	#107	—	2	1	no	—
422	#107	—	2	1	no	—
423	#107	—	2	1	no	—
424	#107	—	2	1	no	—
425	#107	—	2	1	no	—
426	#107	—	2	1	no	—
427	#107	D₄×C₁₃	1	1	yes	characteristic
428	#107	D₄×C₁₃	1	1	yes	characteristic
429	#106	—	2	1	no	—
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	—	2	1	no	—
434	#106	D₄×C₁₃	1	1	yes	characteristic
435	#106	D₄×C₁₃	1	1	yes	characteristic
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	#104	—	2	2	no	—
441	#103	—	2	1	no	—
442	#103	—	2	1	no	—
443	#103	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#103	—	2	1	no	—
447	#103	—	2	1	no	—
448	#103	D₄×C₁₃	1	1	yes	characteristic
449	#103	D₄×C₁₃	1	1	yes	characteristic
450	#102	—	2	1	no	—
451	#102	D₄×C₁₃	1	1	yes	characteristic
452	#102	D₄×C₁₃	1	1	yes	characteristic
453	#101	—	2	2	no	—
454	#97	—	2	1	no	—
455	C₄×C₈	—	2	1	no	—
456	#95	—	4	1	no	—
457	C₂×C₁₃	—	2	1	no	—
458	C₂×C₁₃	—	2	1	no	—
459	C₂×C₁₃	—	4	2	no	—
460	C₂×C₁₃	#2449	1	1	yes	characteristic
461	C₂×C₁₃	#3288	1	1	yes	characteristic
462	C₂×C₁₃	#3293	1	1	yes	characteristic
463	#41	—	2	1	no	—
464	#41	—	2	1	no	—
465	#41	C₂×Q₈×C₁₃	1	2	yes	—
466	#41	C₁₃×#41	1	2	yes	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	4	1	no	—
473	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	Q₁₆	—	2	4	no	—
487	SD₁₆	—	2	4	no	—
488	M₁₆	—	2	4	no	—
489	M₁₆	—	2	1	no	—
490	M₁₆	—	2	1	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	1	no	—
493	M₁₆	—	2	1	no	—
494	M₁₆	—	2	1	no	—
495	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
496	M₁₆	C₁₃×#41	1	2	yes	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	—	4	1	no	—
518	C₄⋊C₄	—	4	1	no	—
519	C₄⋊C₄	—	4	1	no	—
520	C₄⋊C₄	—	4	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	8	2	no	—
524	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	4	1	no	—
541	C₄²	—	4	1	no	—
542	C₄²	—	4	1	no	—
543	C₄²	—	4	1	no	—
544	C₁₃	#26406	1	1	yes	characteristic, direct product factor, Sylow
545	C₂³	—	2	1	no	—
546	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
547	Q₈	—	2	1	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	16	1	no	—
553	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
554	D₄	—	2	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	2	1	no	—
557	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	8	1	no	—
577	C₂×C₄	—	8	1	no	—
578	C₂×C₄	—	8	1	no	—
579	C₂×C₄	—	16	1	no	—
580	C₂×C₄	—	16	1	no	—
581	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
585	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
586	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
587	C₈	—	2	2	no	—
588	C₈	—	2	1	no	—
589	C₈	—	2	2	no	—
590	C₈	—	2	1	no	—
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	C₁₃×#539	1	1	yes	characteristic
601	C₂²	D₄²×C₁₃	1	1	yes	characteristic
602	C₂²	C₁₃×#554	1	1	yes	characteristic
603	C₄	—	2	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	2	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
616	C₄	C₁₃×#525	1	1	yes	characteristic
617	C₄	C₁₃×#547	1	1	yes	characteristic
618	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	4	2	no	—
622	C₂	C₁₃×#2449	1	1	yes	characteristic
623	C₂	C₁₃×#3288	1	1	yes	characteristic
624	C₂	C₁₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#3082	C₂	semidirect
5. C₁₃×#2095	C₂	semidirect
6. C₁₃×#2089	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2060	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1922	C₂	semidirect
15. C₁₃×#1857	C₂	semidirect
70. C₁₃×#137	Q₈	semidirect
151. #26406	C₁₃	direct (N × H)
234. #3082	C₂×C₁₃	semidirect
237. #2095	C₂×C₁₃	semidirect
238. #2089	C₂×C₁₃	semidirect
239. #2064	C₂×C₁₃	semidirect
240. #2060	C₂×C₁₃	semidirect
241. #1952	C₂×C₁₃	semidirect
242. #1922	C₂×C₁₃	semidirect
247. #1857	C₂×C₁₃	semidirect
376. #137	Q₈×C₁₃	semidirect
544. C₁₃	#26406	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3083	2
C₁₃×#3082	2
C₁₃×#2947	2
C₁₃×#2913	2
C₁₃×#2095	2
C₁₃×#2089	2
C₁₃×#2064	2
C₁₃×#2060	2
C₁₃×#1952	2
C₁₃×#1922	2
C₁₃×#1908	2
C₁₃×#1882	2
C₁₃×#1866	2
C₁₃×#1859	2
C₁₃×#1857	2
#26406	13

Subgroups — C13×#26406 #15712745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26406 #15712745